Related papers: Decomposition results for multiplicative actions a…
In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic…
Motion polynomials (polynomials over the dual quaternions with nonzero real norm) describe rational motions. We present a necessary and sufficient condition for reduced bounded motion polynomials to admit factorizations into monic linear…
We study qualitative properties of the set of recurrent points of finitely generated free semigroups of measurable maps. In the case of a single generator the classical Poincare recurrence theorem shows that these properties are closely…
Let $(G_n(x))_{n=0}^\infty$ be a $d$-th order linear recurrence sequence having polynomial characteristic roots, one of which has degree strictly greater than the others. Moreover, let $m\geq 2$ be a given integer. We ask for…
Often, polynomials or rational functions, orthogonal for a particular inner product are desired. In practical numerical algorithms these polynomials are not constructed, but instead the associated recurrence relations are computed.…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation…
We construct fast, structure-preserving iterations for computing the sign decomposition of a unitary matrix $A$ with no eigenvalues equal to $\pm i$. This decomposition factorizes $A$ as the product of an involutory matrix $S =…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
The aim of this paper is to prove ergodic decomposition theorems for probability measures quasi-invariant under Borel actions of inductively compact groups (Theorem 1) as well as for sigma-finite invariant measures (Corollary 1). For…
In the paper, we give partition-theoretic results for the coefficients of some mock theta functions and prove their congruence properties. Some recurrence relations connecting the coefficients of the mock theta functions with certain…
We consider the problem of decomposing a regular non-negative function as a sum of squares of functions which preserve some form of regularity. In the same way as decomposing non-negative polynomials as sum of squares of polynomials allows…
A common problem in various applications is the additive decomposition of the output of a function with respect to its input variables. Functions with binary arguments can be axiomatically decomposed by the famous Shapley value. For the…
Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…
We develop a framework to analyse invariant decompositions of elements of tensor product spaces. Namely, we define an invariant decomposition with indices arranged on a simplicial complex, and which is explicitly invariant under a group…
This paper builds and extends on the authors' previous work related to the algorithmic tool, Cylindrical Algebraic Decomposition (CAD), and one of its core applications, Real Quantifier Elimination (QE). These topics are at the heart of…
This article is devoted to the study of the asymptotic behavior of the zero-energy deformations set of a periodic nonlinear composite material. We approach the problem using two-scale Young measures. We apply our analysis to show that…
If a quantum experiment includes random processes, then the results of repeated measurements can appear consistent with irreversible decoherence even if the system's evolution prior to measurement was reversible and unitary. Two thought…
In this work, we establish a representation theorem for multivariable totally symmetric functions: a multisymmetric continuous function must be the composition of a continuous function and a set of generators of the multisymmetric…
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…